When Sailor Moon and Rini use their crystals they essentially commit suicide. (In B.S.S.M. the princess explains that to use the crystal you have to want something enough to risk your own life.)Neo-Queen Serenity then comes in and tells them that since they were so brave they can live again.

When Rini and Serena say good bye, they aren't supposed to cry. In the original they don't cry at all (Some say it's supposed to be a special moment between the Future Neo-Queen and her Daughter). In the DiCed version there are really cheep tears added to make them look like they don't want to leave. If you look at Rini she is smirking/smiling while she is crying.

Special Requirements:

The episode where Sailor Moon and Rini defeat the Dark Man (whatever his name is).

You're kind of vague about which episode this is. I mean if someone wants to check this out for themselves, it'd be pretty hard even with the bit of info you put up, as there are dozens of Sailor Moon episodes...

Two mistakes.
1. DiC did not "chop this episode up." Dialogue was changed, but there was no cuts made to the actual show itself.
2. There are no fake tears. They merely act like they are crying, but they didn't actually animate actual tears.